The quantum version of a non-linear oscillator Hamiltonian with variable mass is given by [1]}
\(H=\frac{1}{2\lambda }\left[-(1+\delta ^{2}x^{2})\frac{d^{2}}{dx^{2}}-2\delta ^{2}x\frac{d}{dx}+\frac{\lambda ^{2}x^{2}}{1+\delta ^{2}x^{2}}\right]\) 
